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Mathematical Physics

Title:Making electromagnetic wavelets II: Spheroidal shell antennas

Abstract: In the companion paper, a coherent charge-current distribution for radiating
electromagnetic wavelets was constructed on an oblate spheroidal surface S_a.
Its main drawback was the necessity of including magnetic along with electric
charges, making the sources impossible to realize. Here we show how this
difficulty can be overcome by using Hertz potentials to generate a
charge-current distribution due solely to bound electric charges. However, this
distribution still appears difficult to realize because it consists of multiple
surface layers on S_a. We show how it can be replaced by a simple volume
distribution on a spheroidal shell. Our method generalizes the usual
construction of equivalent Huygens sources, based on boundary conditions on an
interface between electromagnetic media, by allowing the transition to be
gradual without incurring addition complexity.